Traversing Shape Up Components

In an earlier post,

Minimizing a Large Shape Up Component
, I mention that I can get a shape smaller by traversing the array from different directions.

I have developed a package dedicated to handling all of my traversing, available on github. All of the core patterns are shown on the official traverse-grid page.

I am going to skip a lot of these methods and focus on the methods that work best for optimizing a Shape Up component.

Alternate

Alternate is a simple mutation that horizontally flips every other row. Applied to a horizontal pattern, it creates a pattern that moves back and forth.

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It is the best method for traversing our pacman (actually a three way tie):

alternate, rotated_waterfall, rotated_watertile 28.05% 23 characters /shapeup/>>dc44317c2216359machbb95

Reposition

The reposition method only iterates even indices in the first iteration, and then odd indices in the second.

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It works really well if your data looks like our waffle:

reposition 14.06% 9 characters /shapeup/_]]Abb6-$035-

Bounce

The bounce method bounces back and forth between two indices, both from the beginning incrementing forward and from the end decrementing backward, meeting in the center. It works well on data that has some symmetry. It is the best method for traversing our dollar sign:

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bounce 31.9% 37 characters /shapeup/]]Bkda2k2g93+2^>4+44>a<2+c*el7<e<c<c<8<k

Smooth

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Smooth looks at all adjacent spaces and tries moves toward the next closest index. It can also be straightened.

Smooth (straight)

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It is the best method for traversing our bee:

straight_smooth 20.93% 104 characters /shapeup/]]LrM)$04[11)a]1^R1z1_va{><1(2131`e9i8[p9ld{ij52(f1>14E56m61L8r9yk61b[t]H1_N!(~O1*2)1*)22!(7<H]2435>{332|^1

Waterfall

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The waterfall is the best method for traversing our chair:

waterfall 26.55% 30 characters /shapeup/]]Hobd9gd4kb4i9+4g7+6f3435+5{949o

Diagonal

The diagonal method does not win out very often, but when it does it can be very effective.

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It works very well when traversing our knife:

diagonal 11.76% 46 characters /shapeup/>yx<$0>{<<<$oob2a1741346qqoom>>v2^d2f2n+C2sog2-

Spiral

The spiral method is fairly effective as most data is off around the border and on in the center.

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It is the best method for traversing our yin yang:

spiral 33.05% 39 characters /shapeup/`gg59^6363431a8+2c4275a56*a+^ac1g}b52c86

Diamond

The diamond method is harder to implement than the others. It helps to visualize the entire diamond first:

                  06                  
               05 29 07               
            04 28 48 30 08            
         03 27 47 63 49 31 09         
      02 26 46 62 74 64 50 32 10      
   01 25 45 61 73 81 75 65 51 33 11   
00 24 44 60 72 80 84 82 76 66 52 34 12
   23 43 59 71 79 83 77 67 53 35 13   
      22 42 58 70 78 68 54 36 14      
         21 41 57 69 55 37 15         
            20 40 56 38 16            
               19 39 17               
                  18

In actuality, we trim off the triangles and we get this:

03 27 47 63 49 31 09
26 46 62 74 64 50 32
45 61 73 81 75 65 51
60 72 80 84 82 76 66
59 71 79 83 77 67 53
42 58 70 78 68 54 36
21 41 57 69 55 37 15

And we have to reduce our values to account for all of those gaps:

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It works really well if you want to make a diamond:

The entire url for this diamond is /shapeup/]99EF because it is just 1 on value and 1 off value. The raw data is simply 9,9,40,41.

It is also the best way to traverse our moon:

diamond 29.49% 23 characters /shapeup/]edB+312148989n{335hhda4

Snake

The snake method is a 2x2 alternated vertical variation of the Tile method. It works like the horizontal method but instead of always moving to the right, it wiggles down and up throughout the process covering two rows at a time. It is the best method for traversing our dolphin.

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snake 12.95% 89 characters /shapeup/]]JyVW(1<$0D(A<e2-<4+1Z2NFz2p{|>1k{o+lVt2X>y2PF<A<E<Ig159+d-j2KW(7<e<k+N^u>7>c2lc1g16>n2fb74

Stitch

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Stitch zig zags in pairs along two cell columns until it fills a space. It is the best method for traversing our note (at a two-way tie):

stitch, vertical 17.42% 27 characters /shapeup/]]Iog>iki2g2g*+<24>>ic|}8^um6_

Watertiletiled 1xwidth waterfall

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Watertile (2)tiled 2xwidth waterfall

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watertile2 17.65% 39 characters /shapeup/]]Yrlx{<1^h+9419+91E*u8h1-3+jv$0$0H<5<2~11

Triangle

The triangle method is pretty similar to the diamond method:

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                        08 27 10                        
                     07 26 43 28 11                     
                  06 25 42 57 44 29 12                  
               05 24 41 56 69 58 45 30 13               
            04 23 40 55 68 79 70 59 46 31 14            
         03 22 39 54 67 78 87 80 71 60 47 32 15         
      02 21 38 53 66 77 86 93 88 81 72 61 48 33 16      
   01 20 37 52 65 76 85 92 97 94 89 82 73 62 49 34 17   
00 19 36 51 64 75 84 91 96 99 98 95 90 83 74 63 50 35 18

Trimmed:

06 25 42 57 44 29 12
24 41 56 69 58 45 30
40 55 68 79 70 59 46
54 67 78 87 80 71 60
66 77 86 93 88 81 72
76 85 92 97 94 89 82
84 91 96 99 98 95 90

And reduced:

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It works better than anything else if your shape is this exact type of triangle

The entire url for this triangle is /shapeup/--+9h$0{0i because it is just 1 on value and 1 off value. The raw data is simply 9,17,72,81.

However none of the shapes in my library are smallest using this exact triangle. It's a good thing we can flip the pattern and try the same thing upside down.

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/shapeup/~~+9h$0{0i

The upside down triangle method is the best method for traversing our checkmark (at a two-way tie).

triangle_flipped, vertical 19.35% 24 characters /shapeup/~~gkU{9bd^3899<87G<<8hh|}7